\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.7 - 2D and Surface Function Interpolation
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GradientFittingTraits Concept Reference
2D and Surface Function Interpolation Reference » Concepts

Definition

Sibson gradient fitting functions are parameterized by a traits class that defines the primitives used by the algorithm. The concept GradientFittingTraits defines this common set of requirements.

Has Models:
CGAL::Interpolation_gradient_fitting_traits_2<K>
See also
InterpolationTraits
CGAL::Interpolation_traits_2<K>
Sibson gradient fitting functions
CGAL::sibson_c1_interpolation()
CGAL::farin_c1_interpolation()
CGAL::quadratic_interpolation()

Types

typedef unspecified_type FT
 The number type must follow the model FieldNumberType. More...
 
typedef unspecified_type Point_d
 The point type on which the function is defined and interpolated. More...
 
typedef unspecified_type Vector_d
 The corresponding vector type. More...
 
typedef unspecified_type Aff_transformation_d
 defines a matrix type. More...
 
typedef unspecified_type Construct_vector_d
 A constructor object for Vector_d. More...
 
typedef unspecified_type Construct_scaled_vector_d
 Constructor object for Vector_d. More...
 
typedef unspecified_type Construct_null_matrix_d
 Constructor object for Aff_transformation_d. More...
 
typedef unspecified_type Construct_scaling_matrix_d
 Constructor object for Aff_transformation_d. More...
 
typedef unspecified_type Construct_sum_matrix_d
 Constructor object for Aff_transformation_d. More...
 
typedef unspecified_type Construct_outer_product_d
 Constructor object for Aff_transformation_d. More...
 

Creation

 GradientFittingTraits ()
 default constructor. More...
 

Operations

The following functions that create instances of the above constructor object types must exist.

Construct_vector_d construct_vector_d_object ()
 
Construct_scaled_vector_d construct_scaled_vector_d_object ()
 
Construct_null_matrix_d construct_null_matrix_d_object ()
 
Construct_sum_matrix_d construct_sum_matrix_d_object ()
 
Construct_outer_product_d construct_outer_product_d_object ()
 

Member Typedef Documentation

typedef unspecified_type GradientFittingTraits::Aff_transformation_d

defines a matrix type.

Must provide the following member functions :

Aff_transformation tr.inverse () which gives the inverse transformation, and

Aff_transformation tr.transform( Vector v) which returns the multiplication of tr with v.

typedef unspecified_type GradientFittingTraits::Construct_null_matrix_d

Constructor object for Aff_transformation_d.

Provides :

Aff_transformation_d operator()() which introduces an affine transformation whose matrix has only zero entries.

typedef unspecified_type GradientFittingTraits::Construct_outer_product_d

Constructor object for Aff_transformation_d.

Provides :

Aff_transformation_d operator()(Vector v) which returns the outer product, i.e. the quadratic matrix v \( ^t\)v.

typedef unspecified_type GradientFittingTraits::Construct_scaled_vector_d

Constructor object for Vector_d.

Provides :

Vector_d operator() (Vector_d v,FT scale) which produces the vector v scaled by a factor scale.

typedef unspecified_type GradientFittingTraits::Construct_scaling_matrix_d

Constructor object for Aff_transformation_d.

Provides :

Aff_transformation_d operator()(FT scale) which introduces a scaling by a scale factor scale.

typedef unspecified_type GradientFittingTraits::Construct_sum_matrix_d

Constructor object for Aff_transformation_d.

Provides :

Aff_transformation_d operator()(Aff_transformation_d tr1, Aff_transformation_d tr2) which returns the sum of the two matrices representing tr1 and tr2.

typedef unspecified_type GradientFittingTraits::Construct_vector_d

A constructor object for Vector_d.

Provides :

Vector_d operator() (Point_d a, Point_d b) which produces the vector b - a and

Vector_d operator() (Null_vector NULL_VECTOR) which introduces the null vector.

typedef unspecified_type GradientFittingTraits::FT

The number type must follow the model FieldNumberType.

typedef unspecified_type GradientFittingTraits::Point_d

The point type on which the function is defined and interpolated.

typedef unspecified_type GradientFittingTraits::Vector_d

The corresponding vector type.

Constructor & Destructor Documentation

GradientFittingTraits::GradientFittingTraits ( )

default constructor.

Member Function Documentation

Construct_null_matrix_d GradientFittingTraits::construct_null_matrix_d_object ( )
Construct_outer_product_d GradientFittingTraits::construct_outer_product_d_object ( )
Construct_scaled_vector_d GradientFittingTraits::construct_scaled_vector_d_object ( )
Construct_sum_matrix_d GradientFittingTraits::construct_sum_matrix_d_object ( )
Construct_vector_d GradientFittingTraits::construct_vector_d_object ( )